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CRC Press eBooks

Interference, Diffraction, Refraction, and Reflection via the Dirac Notation

F.J. Duarte

Published Oct 29, 2013• 0 citations
Publisher

Abstract

The interaction of coherent light with a set of slits, in the near field, gives rise to an interference pattern. Refraction is the change in the geometrical path, of a beam of light, due to transmission from the original medium of propagation to a second medium with a different refractive index. One of the beauties of the Dirac description of optics is the ability to continuously describe the evolution of the interferometric distribution, as it moves from the near to the far field, with a single mathematical equation. The interferometric distribution, in the near field, is mainly part of a single order. At the boundaries there is an incipient indication that of emerging orders. Explicitly, if a mirror is placed at an infinitesimal distance immediately behind the N-slit array then the transmission interferometer becomes a reflection interferometer.

DOI
10.1201/b16055-5

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The interaction of coherent light with a set of slits, in the near field, gives rise to an interference pattern. Refraction is the change in the geometrical path, of a beam of light, due to transmission from the original medium of propagation to a second medium with a different refractive index. One of the beauties of the Dirac description of optics is the ability to continuously describe the evolution of the interferometric distribution, as it moves from the near to the far field, with a single mathematical equation. The interferometric distribution, in the near field, is mainly part of a single order. At the boundaries there is an incipient indication that of emerging orders. Explicitly, if a mirror is placed at an infinitesimal distance immediately behind the N-slit array then the transmission interferometer becomes a reflection interferometer.
Quantum interference, which is a physical phenomenon, and probability amplitudes à la Dirac are miraculously like synonyms. Indeed, the way probability amplitudes are written down on paper is very much as a single photon, or an ensemble of indistinguishable photons, propagates from one plane to the next. And then, if at one of the planes an N -slit array alternative is offered then the probability amplitude notation à la Dirac cleverly describes the N -path alternative via a mathematical summation. Here we should emphasize that since the photon is a nonlocal quantum entity, all the microscopic slits in the N -slit array, or transmission diffraction grating, are illuminated simultaneously.
The genesis of quantum optics can be found in the Dirac discussion on interference as disclosed in The Principles of Quantum Mechanics . This is a masterful and prophetic discussion that begins by considering a roughly monochromatic light source. The discussion continues by considering a beam of light consisting of a large number of photons. Besides Dirac, useful references on interferometry include Steel, Meaburn and Born and Wolf. The Hanbury Brown–Twiss effect originates in interferometric measurements performed by an “intensity interferometer” used for astronomical observations. A diagram of the stellar intensity interferometer used to determine the diameter of stars is depicted. Two-beam interferometers are optical devices that divide and then recombine a light beam. It is on recombination of the beams that interference occurs. The most well-known two-beam interferometers are the Sagnac interferometer, the Mach–Zehnder interferometer, and the Michelson interferometer.
The interpretation of the detection of very slow rate of photo counts in interference and diffraction experiments have given rise to the prevailing interpretation that photons interfere by themselves and they are indivisible, albeit non-local. The purpose of this paper is to inspire the development of alternate models for the photons by underscoring that, in reality, light does not interfere with light. The effects of superposition, registered as interference fringes, can become manifest only when a suitable detector can respond simultaneously to all the superposed light beams separately arriving from all the paths (or, slits). It should be a strictly causal process. In fact, different detectors with different quantum properties, report different results while exposed to the same superposed fields. Interference and diffraction effects are always observed as fringes through the processes of re-distribution and/or re-direction of the measured energy of the superimposed fields. Accordingly, we present a number of experiments, actual and conceptual, which highlight the contradictions built into the notion of non-locality in interference. A closer examination of these experiments can guide us to develop a conceptually congruent and causal model for both the evolution of photons and the interference (diffraction) effects by adapting to the classical diffraction theory. This theory has been correctly predicting the characteristics of light whether it is star light propagating through the inter galactic space, or nano tip generated light propagating through complex nano photonic waveguides.